Calculus is the branch of mathematics used by engineers, physicists, weather forecasters, aircraft designers, astronauts, scientists, and others to develop theories, solve practical problems, and help understand and predict natural phenomena. Calculus provides the answer to questions that can not be solved by using only algebra, geometry, or trigonometry. This course explains the derivation of a function, the applications of derivatives, the integral and how to use it, and methods of integration.
Course Description
The course includes four study units: Calculus: Functions and Use, Parts 1 – 4. There are numerous self-tests (with answers) and four exams.
Also included: Answer Key Supplement, with solutions to the Practice Exercise problems in the study units.
Course Objectives
Upon completion of this course, students will be able to:
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Explain what is meant by the derivative of a function
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Discuss how the derivative can be used in practical applications
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Calculate derivatives, rates of change, velocities, values of a function, etc.
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Calculate the integral, or antiderivative, of simple and compound algebraic functions
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Solve simple differential equations
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Use the integral to calculate distance when velocity is known, the area under a curve,
the area bounded by a curve and a line, volume, hydrostatic pressure, etc.
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Use the chain rule to calculate derivatives of certain functions
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Calculate the derivative of any trigonometric function, any exponential function with
base e, any natural logarithmic functions, and any hyperbolic function
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Calculate the angle that a tangent line to a curve at a point makes with the point’s
radius vector
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Calculate the angular acceleration of a line when its angular position is defined as a
function of time
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Calculate integrals involving exponentials, trigonometric functions, hyperbolic
functions, and inverse trigonometric functions
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Calculate integrals by means of integration by parts
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Calculate the area bounded by a curve described by parametric or polar equations
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Calculate the length of a curve, the centroid of an area, and both the average value
and the RMS value of a function
Course Outline
Study Unit 1: Calculus: Functions and Use, Part 1
Introduction; Polynomial Functions; Other Functions of X; Using the Greek Alphabet; Formal Definition of a Function; Inverse Functions; Continuous Functions; Limits; Calculating Average Rate of Change; Calculating Exact Rate of Change; Derivative; Differentiation; Geometric Interpretation of Derivative; Common Formulas Used in Differentiation; Compound Functions; Derivative of a Product; Derivative of a Quotient; Applications of the Derivative; Acceleration; Applications of Derivatives to Electricity
Study Unit 2: Calculus: Functions and Use, Part 2
Introduction to the Integral; Rules for Integration; Integrals of Compound Functions; Elementary Applications; Definite and Indefinite Integrals; Interpretation of Negative Areas; Application of Integral to Electrical Quantities; Differential Equation; Applications of Differentials; Tips for Solving Problems Involving Integration; Integration by Parts
Study Unit 3: Calculus: Functions and Use, Part 3
Common Formulas for Derivatives; Implicit Functions and Parametric Equations; Derivatives of Trigonometric Functions; Derivatives of Exponential and Logarithmic Functions; Applications of Derivative; Derivatives of Hyperbolic Functions
Study Unit 4: Calculus: Functions and Use, Part 4
Basic Formulas for Derivatives; Corresponding Formulas for Integrals; How to Calculate Integrals Involving Logarithms, Exponentials, Trigonometric Functions and Their Inverses, Hyperbolic Functions, and Integration by Parts; Other Methods to Calculate Area; How to Calculate Moments of an Area, Centroid of an Area, Area of Surface of Revolution, Center of Gravity of Solids, Average Value of a Function, and RMS Value of a Function
How it Works
After registering for the Calculus course, all of your learning materials will be shipped directly to you. If you like, you can also go to our website and download some of your study materials to get a head start. Your learning materials will guide you through the course content, explaining concepts and operations through a series of lessons. After each lesson, you’ll take an exam which you can submit by phone or our website. As you pass each lesson, you’ll proceed to the next topic until you complete the course.
There are four exams that need to be passed to complete your course in Calculus and you’ll have up to 15 weeks to complete the course.
Support
If you should ever need help with your studies, you can e-mail or call our instructors who will gladly help you with any questions that you might have.
Study Time
Since there is no set class schedule, you study when and where it’s convenient for you. You can complete your course as quickly as you’d like.
Completion
When you have successfully completed your course, you will receive a letter of completion along with an official transcript listing your completed course(s) and grades. You can apply your course towards our Diploma Program or a diploma from your local High School (be sure to check with your school authorities regarding mandatory attendance policies and whether they agree that the Penn Foster High School Program is acceptable toward the completion of your high school education).
Accreditation
Penn Foster High School is accredited by The Middle States Commission on Secondary Schools; has met the high standards of integrity and performance set by the Accrediting Commission of the Distance Education and Training Council (DETC), Washington D.C., and is licensed by the Pennsylvania State Board of Private Licensed Schools.
Whether you’re looking for accelerated studies or credit recovery, regionally and nationally accredited Penn Foster High School provides the courses you need to complete your High School Diploma.
